th order neutral differential equations with properties and .
-th order ordinary differential systems under Stieltjes boundary conditions
-widths for singularly perturbed problems
-widths for singularly perturbed problems
Kolmogorov -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.
Nachweis periodischer Lösungen in nichtautonomen Systemen mit Hilfe des Brouwerschen Fixpunktsatzes
Natural and artificially controlled connections among steady states of a climate model.
Natural boundary value problems for weighted form laplacians
The four natural boundary problems for the weighted form Laplacians acting on polynomial differential forms in the -dimensional Euclidean ball are solved explicitly. Moreover, an algebraic algorithm for generating a solution from the boundary data is given in each case.
Natural Runge-Kutta and Projection Methods.
Near viability for fully nonlinear differential inclusions
We consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness...
Necessary and Sufficient Condition for Oscillations of Neutral Differential Equation
2000 Mathematics Subject Classification: 34K15, 34C10.We obtain necessary and sufficient conditions for the oscillation of all solutions of neutral differential equation with mixed (delayed and advanced) arguments ...
Necessary and sufficient conditions for a system of eigenfunctions and associated functions of a Sturm-Liouville operator with discontinuous coefficients to possess the basis property.
Necessary and sufficient conditions for bounded oscillations of higher order delay differential equations of Euler's type
Necessary and sufficient conditions for eventually vanishing oscillatory solutions of functional equations with small delays.
Necessary And Sufficient Conditions For Existence Of Solutions To Equations With Noninvertible Linear Part.
Necessary and sufficient conditions for finally vanishing oscillatory solutions in second order delay equations
Necessary and sufficient conditions for global-in-time existence of solutions of ordinary, stochastic, and parabolic differential equations.
Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability
For general matrix summability methods, we find necessary and sufficient conditions for such methods to be stronger than multisummability. In a second part we show the existence of power series which are not multisummable but can be summed by a matrix method satisfying the conditions mentioned above
Necessary and sufficient conditions for oscillation of delay equations with constant coefficients
Necessary and sufficient conditions for oscillation of neutral equation
Necessary and sufficient conditions for oscillation of second-order differential equations with nonpositive neutral coefficients
In this work, we present necessary and sufficient conditions for oscillation of all solutions of a second-order functional differential equation of type where . Under the assumption , we consider two cases when and . Our main tool is Lebesgue’s dominated convergence theorem. Finally, we provide examples illustrating our results and state an open problem.